COUPLING POPOV'S ALGORITHM WITH SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING EQUILIBRIUM PROBLEMS

Based on the recent works by Censor et al. [The subgradient extragradient method for solving variational inequalities in Hilbert space. J. Optim. Theory Appl. 148, 318-335 (2011)], Malitsky and Semenov [An extragradient algorithm for monotone variational inequalities. Cybern. Syst. Anal. 50, 271-277 (2014)], and Lyashko and Semenov [A new two-step proximal algorithm of solving the problem of equilibrium programming, In: Optimization and Applications in Control and Data Sciences (ed. B.Goldengorin), Springer Optimization and Its Applications, volume 115, 315-326 (2016)], we propose a new scheme for solving pseudomonotone equilibrium problems in real Hilbert spaces. Weak and strong convergence results are suitably established. Our algorithm improves the recent one announced by Lyashko and Semenov not only from computational point of view, but also in some assumptions imposed on their main result. A comparative numerical study is carried out between the algorithms of Quoc-Muu-Nguyen [Extragradient algorithms extended to equilibrium problems. Optimization 57, 749-776 (2008)], Lyashko-Semenov, and the new one. Some numerical examples are given to illustrate the efficiency and performance of the proposed method.